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• Unknot (category 0 genus knots and links)
  seen as a trivial knot In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the
  5 KB (560 words) - 19:08, 6 February 2024
• Knot theory (category Knot theory) (section Adding knots)
  billion knots and links (Hoste 2005). The sequence of the number of prime knots of a given crossing number, up to crossing number 16, is 0, 0, 1, 1, 2
  48 KB (6,198 words) - 19:12, 6 February 2024
• Link (knot theory) (section Tangles, string links, and braids)
  each strand required to lie at (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), ... – i.e., connecting the integers, and ending in the same order that they
  8 KB (1,104 words) - 22:45, 6 February 2024
• Figure-eight knot (mathematics) (category 1 genus knots and links)
  generalizing Thurston's construction to other knots and links. The figure-eight knot is also the hyperbolic knot whose complement has the smallest possible
  9 KB (986 words) - 18:54, 6 February 2024
• Borromean rings (category 6 crossing number knots and links) (section Definition and notation)
  In the tables of knots and links in Dale Rolfsen's 1976 book Knots and Links, extending earlier listings in the 1920s by Alexander and Briggs, the Borromean
  42 KB (4,468 words) - 20:52, 8 February 2024
• Knot invariant (category Knot invariants)
  org/stable/1970594.  Rolfsen, Dale (2003). Knots and Links. Providence, RI: AMS. ISBN 0-8218-3436-3.  Adams, Colin Conrad (2004). The Knot Book: an Elementary Introduction
  10 KB (1,266 words) - 00:08, 7 February 2024
• Prime knot (category Knot invariants)
  non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Knots that are not prime are said to be composite knots or composite
  3 KB (288 words) - 21:40, 6 February 2024
• Knot complement (category Knot theory)
  three-sphere taking one knot to the other. Knot complements are Haken manifolds. More generally complements of links are Haken manifolds. Knot genus Seifert surface
  3 KB (284 words) - 17:35, 6 February 2024
• Hyperbolic link (redirect from Hyperbolic knot) (category Hyperbolic knots and links)
  William Menasco. 41 knot (the figure-eight knot) 52 knot (the three-twist knot) 61 knot (the stevedore knot) 62 knot 63 knot 74 knot 10 161 knot (the "Perko pair"
  2 KB (228 words) - 15:55, 6 February 2024
• Jones polynomial (category Knot theory) (section Link with quantum knot invariants)
   175. ISBN 978-0-387-98254-0. https://www.springer.com/mathematics/geometry/book/978-0-387-98254-0.  Thistlethwaite, Morwen (2001). "Links with trivial Jones
  17 KB (2,344 words) - 19:41, 6 February 2024
• Alternating knot (category Knot invariants)
  alternating goes to 0 exponentially quickly. Alternating links end up having an important role in knot theory and 3-manifold theory, due to their complements
  6 KB (693 words) - 16:41, 6 February 2024
• Wild knot (category Knots and links)
  encyclopediaofmath.org/index.php?title=Main_Page  "Quadrisecants of knots and links", Journal of Knot Theory and Its Ramifications 3: 41–50, 1994, doi:10.1142/S021821659400006X 
  2 KB (236 words) - 21:31, 6 February 2024
• (−2,3,7) pretzel knot (category 0 Arf invariant knots and links)
  Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits various interesting phenomena under three-dimensional and four-dimensional
  2 KB (138 words) - 20:13, 6 February 2024
• Berge knot (category Knots and links) (section Knots)
  Yamada, Yuichi (2005), "Berge's knots in the fiber surfaces of genus one, lens space and framed links", Journal of Knot Theory and its Ramifications 14 (2):
  4 KB (408 words) - 18:34, 6 February 2024
• Whitehead link (category 5 braid length knots and links)
  remaining crossings have equal numbers of under and over crossings on each loop, its linking number is 0. It is not isotopic to the unlink, but it is link
  6 KB (622 words) - 16:01, 6 February 2024
• Crossing number (knot theory) (category Knot invariants)
  There are no other knots with a crossing number this low, and just two knots have crossing number five, but the number of knots with a particular crossing
  5 KB (565 words) - 22:45, 6 February 2024
• Alexander polynomial (category Knot theory)
  disks and genus bounds". Geometry and Topology 8 (2004): 311–334. doi:10.2140/gt.2004.8.311.  Ni, Yi (2007). "Knot Floer homology detects fibred knots". Inventiones
  17 KB (2,507 words) - 19:35, 6 February 2024
• Knot group (category Knot invariants)
  square knot and the granny knot have isomorphic knot groups, yet these two knots are not equivalent. Link group Hazewinkel, Michiel, ed. (2001), "Knot and
  3 KB (368 words) - 00:10, 7 February 2024
• List of mathematical knots and links (category Knot theory) (section Knots)
  mathematical knots and links. See also list of knots, list of geometric topology topics. 01 knot/Unknot - a simple un-knotted closed loop 31 knot/Trefoil knot
  3 KB (419 words) - 17:53, 8 February 2024
• Conway notation (knot theory) (category Knot theory)
  Conway, J.H. (1970). "An Enumeration of Knots and Links, and Some of Their Algebraic Properties". in Leech, J.. Computational Problems in Abstract Algebra. Pergamon
  3 KB (363 words) - 20:07, 6 February 2024

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